Assessed Task(s):

Matrices Unit Test (Criterion A)

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Objectives:

Display information in the form of a matrix of any order and interpret the data in a given matrix

Solve problems involving the calculation of the sum and product (where appropriate) of two matrices and interpret the results

Calculate the product of a scalar quantity and a matrix

Use the algebra of 2x2 and 3x3 matrices (including the zero and identity matrix)

Calculate the determinant and inverse of non-singular 2x2 and 3x3 matrices and solve simultaneous linear equations

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As an IB Learner you are reflective. On one page of your blog you will need to explain each of these important ideas in your own words:

1. Systems of equations (graphing, substitution, and addition)

2. Four elementary row operations

3. Process of pivoting

4. Gauss-Jordan elimination

5. Matrix operations

6. Properties of matrices

7. Inverse of a matrix

8. Systems of inequalities

9. Linear programming theorem

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TYPES OF PROBLEMS YOU WILL NEED TO SOLVE:

• Solve systems of equations by graphing, substitution, or addition, as directed.

• Solve systems of equations by selecting the most appropriate method.

• Solve applied problems, including coin problems, combining rates, supply and demand, and mixture problems.

• Know the relationship between a system of equations and a corresponding matrix

• Perform elementary row operations on a given matrix.

• Solve systems of equations by the Gauss-Jordan method.

• Carry out matrix operations, including finding the inverse of a given matrix.

• Solve a system of equations using the inverse matrix method.

• Solve a system of inequalities.

• Decide whether a given point is a feasible solution for a set of constraints.

• Decide whether a given point is a corner point for a set of constraints.

• Find the corner points for a set of feasible solutions.

• Maximize or minimize an objective function subject to a set of constraints.

• Solve applied problems using a linear programming model.

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Systems of Linear Equations

Video:

Solving linear equations using graphing (time: 3:57)
Solving linear equations using substitution (time: 8:11)
Solving linear equations using addition (time: 9:59)

Reference Topic Sites:

This site gives a nice review of solving simple systems of equations.
http://www.purplemath.com/modules/systlin1.htm

This site gives a review of solving simple systems of equations by adding with links to solving simple systems using other methods. This is a great site if you take this link along with the other links provided at this site.
http://www.analyzemath.com/Tutorial-System-Equations/Tutorial-System-Equations.html

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Problem Solving with Systems

Reference Topic Sites:

Reviews translating word problems into systems of equations.
http://www.purplemath.com/modules/systprob.htm

Use the calculator on this site to solve the system of equations that you obtain from the word problems in this section.
http://www.analyzemath.com/Calculators/Calculator_syst_eq.html

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Matrix Solution of a System of Equations

Gauss:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Gauss.html



Jordan:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Jordan.html

Video:

Solving Systems Using Matrices (time: 9:58)

Reference Topic Sites:

This site gives a Gauss-Jordan Elimination Program:
http://www.nevada.edu/~jfm/finite/inverse/gaussian.htm#top

This site is for the TI-83 graphics calculator but it applies to a wide range of calculator models:
http://www.wvup.edu/cbrady/GaussJordan.pdf

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Inverse Matrices

Cayley:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Cayley.html



Sylvester:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Sylvester.html

Video:

Solving Systems of Equations Using Inverses (two variables) (time: 6:27)

Reference Topic Sites:

Matrix multiplication site:
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/frames3_2.html

Interactive site discussing matrix addition:
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/frames3_1.html

Interactive matrix multiplication site:
http://www.cogs.indiana.edu/software/linalg/vectorMatrix/

Interactive site discussing inverse matrices:
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/tutorialsf1/frames3_3.html

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Modeling with Linear Programming

Video:

Graphing Systems of Linear Inequalities (time: 5:16)
Linear Programming (time: 11:10)

Reference Topic Sites:

An overview of linear programming:

http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/Summary4.html